1. **Problem:** Sketch a rotation angle $\theta$ in the second quadrant with a reference angle of $70^\circ$. Then state the measures of $\theta$ and another positive angle less than $360^\circ$ with the same cosine value. 2. **Step 1:** Understand that the second quadrant angles range from $90^\circ$ to $180^\circ$. 3. **Step 2:** The reference angle is the acute angle between the terminal side of $\theta$ and the x-axis. For the second quadrant, $\theta = 180^\circ - \text{reference angle}$. 4. **Step 3:** Calculate $\theta = 180^\circ - 70^\circ = 110^\circ$. 5. **Step 4:** The cosine of $\theta$ is negative in the second quadrant. To find another positive angle less than $360^\circ$ with the same cosine value, use the fact that cosine is positive in the fourth quadrant and symmetric about the x-axis. 6. **Step 5:** The other angle is $360^\circ - 110^\circ = 250^\circ$. --- **Final answers:** - $\theta = 110^\circ$ - Another positive angle with the same cosine: $250^\circ$